| 1–9: One-Dimensional Problems |
| 1 | Course Outline; Free Particle; Motion (PDF) |
| 2 | Infinite Box, \(\delta(x)\) Well, \(\delta(x)\) Barrier (PDF - 1.0MB) |
| 3 | Probability Density: Motion, Position, Spreading, Gaussian Wavepacket (PDF - 1.6MB) |
| 4 | Stationary Phase and Gaussian Wavepackets (PDF) |
| 5 | Continuum Normalization (PDF) |
| 6 | Linear Potential; JWKB Approximation and Quantization (PDF - 1.4MB) |
| 7 | JWKB Quantization Condition (PDF - 1.1MB) |
| 8 | Rydberg-Klein-Rees: \(V(x)\) from \(E_{vJ}\)(PDF - 1.4MB) |
| 9 | Numerov-Cooley Method: 1-D Schrödinger Equation (PDF) |
| 10–19: Matrix Mechanics |
| 10 | Matrix Mechanics (PDF - 1.1MB) |
| 11 | Eigenvalues, Eigenvectors, and Discrete Variable Representation (PDF - 1.1MB) |
| 12 | Matrix Solution of Harmonic Oscillator I (PDF - 1.1MB) |
| 13 | Matrix Solution of Harmonic Oscillator II (PDF - 1.3MB) |
| 14 | Perturbation Theory I (PDF - 1.2MB) |
| 15 | Perturbation Theory II (PDF - 1.2MB) |
| 16 | Perturbation Theory III (PDF - 1.2MB) |
| 17 | Perturbation Theory IV (PDF - 1.1MB) |
| 18 | Variational Method (PDF) |
| 19 | Density Matrices I (PDF) |
| 20–29: Central Forces and Angular Momentum |
| 20 | Density Matrices II (PDF - 1.0MB) |
| 21 | 3-D Central Force Problems I (PDF - 1.5MB) |
| 22 | 3-D Central Force Problems II (PDF - 1.6MB) |
| 23 | Angular Momentum Matrix Elements from Commutation Rules (PDF) |
| 24 | J-Matrices (PDF - 1.3MB) |
| 25 | HSO + HZeeman: Coupled vs. Uncoupled Basis Sets (PDF - 1MB) |
| 26 | HSO + HZeeman in ⎜JLSMJ\(\rangle\) and ⎜LMLMS\(\rangle\) by Ladders plus Orthogonality (PDF) |
| 27 |
Wigner-Eckart Theorem (PDF - 1.2MB)
Lecture 27 Supplement 1: Angular Momentum Eigenvalues (PDF) (Courtesy of Dudley Herschbach. Used with permission.)
Lecture 27 Supplement 2: Simplification of hyperfine Hhf by Wigner-Eckart Theorem (PDF)
Lecture 27 Supplement 3: A User’s Guide to Angular Momentum Theory (PDF - 2.2MB)
|
| 28 | Hydrogen Radial Wavefunctions (PDF - 1.1MB) |
| 29 | Begin Many-Electron Atoms: Quantum Defect Theory (PDF - 1.0MB) |
| 30–39: Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice |
| 30 | Matrix Elements of Many-Electron Wavefunctions (PDF - 1.3MB) |
| 31 | Matrix Elements of One-Electron, \(F(i)\), and Two-Electron, \(G(i,j)\) Operators (PDF - 1.2MB) |
| 32 | Configurations and Resultant L–S–J States (PDF - 1.4MB) |
| 33 | L-S Terms via L2, S2 and Projection (PDF - 1.0MB) |
| 34 | \(e^2/r_{ij}\) and Slater Sum Rule Method (PDF - 1.3MB) |
| 35 | Spin Orbit: Many Electron ζ(N,L,S)↔Single Orbital ζ\(_{nl}\) Coupling Constants (PDF - 1.2MB) |
| 36 | Holes; Hund's Third Rule; Landé g-Factor via W-E Theorem (PDF) |
| 37 | Infinite 1-D Lattice I (PDF - 1.0MB) |
| 38 | Infinite 1-D Lattice II (PDF - 1.1MB) |
| 39 | One-Dimensional Lattice: Weak-Coupling Limit (PDF - 1.0MB) |
